The Real Madrid star has been linked with a move away from the Bernabeu next summer, with the likes of Manchester United and PSG leading the chase to land the current world footballer of the year.
However, according to AS, Chelsea owner Roman Abramovich is willing to trump other European heavyweights by offering Real £70m.
Abramovich has a good relationship with Ronaldo's agent, Jorge Mendes, and will attempt to lure the Portuguese to Stamford Bridge after the European Championships next summer.
Chelsea boss Jose Mourinho is also understood to be fully behind the pursuit of Ronaldo, having worked with his compatriot during his three seasons in charge at the Bernabeu.
